Theory:

The pattern of rhymes at the ending of each line in a poem is called a rhyme scheme. Letters (A,B,C...) are usually used to express which lines rhyme. Verses that are designated with the same letter are said to rhyme with each other. It is also known as an arrangement of rhymes in a stanza or a poem.
Example:
For easier understanding of the concept, let us take a poem "Neither out far nor in deep", written by Robert Frost as an example.
 
The people along the sand
All turn and look one way.
They turn their back on the land.
They look at the sea all day.
 
We see that the first and third lines rhyme with each other (sand - land); the second and fourth lines rhyme with each other (way - day). Let us name each line as \(A\), \(B\), \(C\) & \(D\) depending on the words that rhyme with each other.
 
The people along the sand
\(A\)
All turn and look one way.
B
They turn their back on the land.
\(A\)
They look at the sea all day.B
 
It can thus be seen that this poem follows \(ABAB\) pattern.
Rhyme scheme of the poem "The Quarrel":
I quarrelled with my brother
A
I don’t know what about,
 B 
One thing led to another
 A 
And somehow we fell out.
B
The start of it was slight,
C
The end of it was strong,
D
He said he was right,
C
I knew he was wrong!
D
It can thus be seen that this poem also follows the ABAB pattern. The last four lines follow the CDCD pattern as the rhyming words are different from ABAB - the first set of rhyming words.